Is there any relation between the rank and the number of zero eigenvalues?
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Welcome to MSE. Please let us know about your attempts in trying to solve this problem when asking a question. You should also provide information on the context and why you are interested in this. – Jan 09 '19 at 17:10
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You can refer to https://en.wikipedia.org/wiki/Rank%E2%80%93nullity_theorem – Mostafa Ayaz Jan 09 '19 at 17:14